Mental math in consulting & case interview

Becoming a consultant does not necessitate being a mathematical expert or holding a math degree. However, having solid mathematical skills is actually quite crucial for success in this field.

Mental math, in particular, is crucial. It's not only important for interviews but also extremely helpful in your daily work. However, mastering mental math takes time and a structured approach. Here's some valuable information to help you get started on developing this skill.

Why is mental math a must-have skill to become a consultant?

Because you will not be allowed to use calculator in the interview

In the case interview, you will not be allowed to use a calculator. Speed becomes paramount, and while exact precision is not an absolute necessity, you must be able to provide quick, reasonably accurate answers. 

Interviewers won't wait around for extended calculations. Hence, using mental math is a necessary skill for anyone aspiring to join a consulting firm, particularly due to its integral role in the case interview. 

Mental math is not a separate part of the case interview, it's threaded throughout the entire process. At every step of a case calculation, you'll be required to perform rapid mental calculations. Your ability to tackle mathematical challenges on the fly is paramount. 

Interviewers can also observe how candidates use mental math to solve problems to evaluate their mental acumen. The sharper your mental math proficiency, the more points you will score in interviewer eyes.

Because consultants work with numbers everyday

Additionally to case interviews, the consulting industry as a whole also places a high value on mathematical ability. A strong foundation in math is essential for consultants to effectively tackle the myriad challenges they face daily.

Mental calculation takes on an even greater significance. It becomes a time-saving tool, helping you swiftly analyze data and offer insights. 

Beyond efficiency, it's also a credibility builder. Since you can quickly estimate numbers and make reasonably accurate calculations in your head, it earns the trust and respect of those you work with.

Nevertheless, in consulting job, precision is not always the ultimate goal. Accuracy around the 95% mark is generally acceptable, but speed is paramount. 

At first, you might not be very familiar with this mental calculation, but if you really aspire to become a consultant, you will need to learn this skill.


How to do mental math for consulting?

As mentioned above, calculations in consulting do not require you to give absolutely accurate results, you have about 5% margin for error. Thus, you can always trade a tiny bit of accuracy for a lot more speed.

Below I will introduce to you a methodical approach to mental calculations with large numbers in a short time. If you can get the hang of it, this technique is actually quite straightforward and extremely useful.

You can apply this method for multiplication, division, and percentage:

Step 1: Estimation

  • Simplify the large numbers by taking out the zeroes 

(example: 6,700,000 → 6.7 & 000000)

  • Round the resulting 1-to-2-digit numbers for easier calculations 

(example: 6.7 → 7)

Step 2: Adjustment

  • Perform simple calculations with the multiplicands
  • Adjust in the opposite direction of the previous rounding and put the zeroes back in

Step 3: Percentages (only for percentages case)

  • To do percentages, multiply the original number with the numerator then divide by 100

Example 1 - Multiplication: 1,234 x 5,678

  • Take out zeroes: 12.34 x 56.78 | 00 00

  • Round: 12 x 60 | 00 00

  • Calculate: 720 | 0 000

  • Adjust and add zeros: 7,200,000 (equal down-rounding and up-rounding roughly cancels each other out)

→ Accurate result: 7,006,652 | Error margin: 2.7%

Example 2 - Division: 8,509 / 45

  • Take out zeroes: 85 / 4.5 | 00 / 0

  • Round: 90 / 4.5 | 00 / 0

  • Calculate: 20 | 0

  • Adjust and add zeros: 190 (up-rounding means downward adjustment)

→ Accurate result: 189.09 | Error margin: 0.48%

Example 3 - Percentage 70% of 15,940

  • Convert %: 0.7 x 15,940

  • Take out zeroes: 7 x 15.9 | One 0 in, three 0 out

  • Rounding: 7 x 16 | One 0 in, three 0 out

  • Calculate: 112 | One 0 in, three 0 out

  • Add zeros: 11,200

  • Adjust : 11,150 (up-rounding means downward adjustment)

→ Accurate result: 11,158 | Error margin: 0.07%

For percentage calculations, it is even easier with the “Zeroes management”. We know that the final answer will have roughly the same number of digits as the original 15,940, something like 1x,xxx or x,xxx. So when having 112 after step “Calculate”, we know the final answer would be close to 11,200.


Common mental math mistakes

Excess or missing zeroes

Adding an extra zero or accidentally omitting one might appear as a minor mistake, but in a case interview, it can lead to substantial miscalculations. 

When working through calculations in your head, it's tempting to overlook those zeroes, especially when simplifying numbers. However, this seemingly simple error can throw off the entire analysis.

Losing one single zero in any step can make your answer meaningless and confusing, which could lead to wrong conclusions. Hence, to safeguard against this pitfall, stay vigilant about place value and ensure each digit is accurately considered. 

A helpful strategy is to reduce metrics to their simplest form, using terms like "7M" for "7,000,000". This not only streamlines your calculations but also reduces the likelihood of confusion. Still, just remember to reintroduce the units in your final results for clarity and accuracy.

Confusion between units

In the high-pressure context of consulting, where time is limited and stress is high, unit conversions can quickly become a minefield. Whether you're switching currencies, time zones, or any other type of measurement, it's crucial to remain vigilant. 

One common pitfall is forgetting to correctly convert units, for instance, one data source uses kilometers, while another uses meters (where it should also be kilometers). Such errors can result in grossly inaccurate results. 

To safeguard against this, always double-check your unit conversions to guarantee the precision of your units. 

Forgetting the real answer

In a consulting case interview, it's vital to be aware that the math you perform is a means to an end, not the end itself. Calculations are a tool used to address more extensive business challenges. 

You may have a solid grip on the math, but if your answer doesn't address the problem you're trying to resolve, it's all for nothing. 

Staying focused is the key. After every calculation, take a moment to ensure your answer aligns with the question at hand. 

One helpful approach is to write down the initial question at the top of your paper before diving into your calculations. As you work through your math and prepare to present your solution, keep reminding yourself of the original question. 

This habit ensures that your calculations are always directly addressing the core problem.


Tips and Tricks for mental math

Don't insist that mental math is only in your head, write it down 

One common misconception about mental math is that it should be entirely performed in your head. However, there's no shame in writing things down. 

While mental math implies doing calculations mentally, there's no rule against jotting down numbers and intermediate steps. 

Many seasoned consultants find it useful to note down key numbers and calculations. This not only reduces the cognitive load but also minimizes the risk of errors.

Writing things down also can help you avoid errors and keep your thoughts organized. In fact, consultants often use scratch paper during solving cases to ensure accuracy.

Shorten the complexity

Simplify calculations as much as possible, rounding numbers to make them more manageable. For instance, if you need to calculate 18% of 68, you can round these to 20% of 70, which is much easier. Then adjust for the rounding to get a close estimate.

In consulting, time is often in short supply, and simplicity is your ally. When faced with complex calculations, break them down into smaller, more manageable parts. Simplify numbers or round them to make the math more accessible. 

By chunking a complex problem into smaller, solvable pieces, you can navigate through it with greater speed and precision.

Sanity check is a must 

Consulting projects and case interviews can be intense. The pressure to perform can lead to overlooked errors. That's where the sanity check comes in. 

After performing your mental calculations, perform a quick "sanity check" to ensure your answer aligns with your logic, you can compare the outcome with another obvious data.

After completing a mental math calculation, take a moment to ensure it makes sense. Does the answer align with your expectations and the context of the problem? 

If 60% of 24,750 equals 475,800, perhaps something is wrong with your “zeroes management”.

A quick review can catch mistakes before they become costly errors.

Practicing is the code!

Above all, mental math is just a skill that you can learn once you know the method and spend time practicing. Take your time to get familiar with the mental calculation method that I mentioned above. It is quite simple and I believe everyone can do it. 

Hence, apply this method while practicing, you will quickly master consulting mental math soon

If you are looking for a tool to practice mental math, I highly recommend using our mental math practice tool. It's totally free! You just need to register and login to use.

This free mental math tool is just a part of our “Comprehensive Math Drills” package, which includes study materials and comprehensive math practice tools for case interviews. For additional practice with consulting math, you can find more here: Comprehensive Math Drills

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